I investigated this when I used to grow. It's my understanding that you use dry ice for rapid drying of fresh bud, not to cure it. Dry ice removes moisture from the bud faster, but curing weed involves putting it into an air tight container so that the chlorophyl breaks down over time, along with any other chemistries that make it a harsher smoke, until you are left with a smoother product.
For drying, you place into a container with holes poked in the top an equal amount of fresh bud and dry ice, then put it in the freezer. Make sure the bud is not physically touching the dry ice or it might damage it. You then remove the bud after 3-7 days. This is considered a rapid method of drying, just like heating it on low heat in the stove would be. You should only do this is if you really need the bud to be ready fastt as some quality will be compromised. The best method of drying is still just letting it sit out in a well ventilated space.